If I create an appointment in the Android* calendar application, I can add a reminder that will pop-up on my phone at the configured time. It will automatically synchronise the event with Google Calendar (which is great!).

If I create the appointment with Google Calendar, I can add a reminder that will either be sent as an email, be sent as a text message or appear as a web-browser pop-up. Again, the event will be synchronised with the phone. I really like the Google Calendar email notifications as they appear in Gmail Manager as well as on the phone, so I'm much more likely to notice the reminders when I'm at work and have my phone on silent.

Is there any way to create an appointment in the Android calendar application and at the same time set up a reminder to come by email rather than as a calendar reminder notification?

Most mobile devices with calendar applications support pop-up reminders and may chime and show a an alert to notify you of the event. I prefer this method so that I can specify a special sound for calendar notifications vs normal emails, but this is where you would create an email notification.

It seems you want to remove the pop-up notifications, and add an email notification.

You can create a new calendar and adjust it's notifications if you don't want to receive an email for every event/only want email notifications for specific events.

But you've said in the beginning of the post that it can be done by using calendar website. Correct me if I'm wrong or misunderstood you.
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roxanApr 12 '12 at 3:37

It's a one time process that may require login to the website. I am unsure as to whether these detailed options are available within the calendar app itself, but are definitely available and only need to be set up a single time within the web interface.
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earthmeLonApr 13 '12 at 1:39